EM superposition [complete image synthesis?]

Readers, please bare with me as I attempt to explain the reasoning of my question. Any help will be greatly appreciated.

Suppose I turn on my radio. And suppose one of my favorite songs happens to be playing, and that song happens to include the tried and true guitar, bass and drum trio. My understanding of Fourier analysis tells me that I should be able to mathematically 'separate' these instruments from the whole (the complex wave) and, furthermore, be able to break these singled-out instruments into even simpler pure tones. Likewise, with the proper parameters I should be able to recreate the entire song on the pure-tone level. All this keeping in mind that sound is linear as percieved by humans (assuming that one ear is covered) due to the mechanizations of the inner ear.

Now, as I type this, I am viewing a scene processed two dimensionally [when I close one eye]. Are the monitor, books, pencils, and other objects analogous to the instruments of the song from the radio? Could I pull these objects out, and break them down even further into a series of simple waveforms? Is it possible to *synthesize* a scene with a series of simple waveforms? The concept of the 'pinhole' camera suggests so. Where the light converges to a single point suggests that at that point an entire scene can be expressed as a single complicated wave [or a fraction of]. What type of equipment could generate these waves; say for transmission through optical fibers [the 'pinhole']?

in any number of dimensions. You could use such a transform to represent any part of a two dimesional image, but the problem is separating the image of a pencil from the image of a piece of paper. Even the one dimensional problem of separating tones is not as simple as you think it is. The one dimensional transform changes from a time representation to a frequency one, but our ears and brain don't really do a fourier transform, they do one that is in between, some time and some frequency, so to speak.